Problem: There is a light source on the plane. This source is so small that it can be represented as point. The light source is moving from point (a, s_y) to the (b, s_y) (s_y < 0) with speed equal to 1 unit per second. The trajectory of this light source is a straight segment connecting these two points. 

There is also a fence on OX axis represented as n segments (l_i, r_i) (so the actual coordinates of endpoints of each segment are (l_i, 0) and (r_i, 0)). The point (x, y) is in the shade if segment connecting (x,y) and the current position of the light source intersects or touches with any segment of the fence.

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You are given q points. For each point calculate total time of this point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y).

Input

First line contains three space separated integers s_y, a and b (-10^9 ≤ s_y < 0, 1 ≤ a < b ≤ 10^9) — corresponding coordinates of the light source.

Second line contains single integer n (1 ≤ n ≤ 2 ⋅ 10^5) — number of segments in the fence.

Next n lines contain two integers per line: l_i and r_i (1 ≤ l_i < r_i ≤ 10^9, r_{i - 1} < l_i) — segments in the fence in increasing order. Segments don't intersect or touch each other.

Next line contains single integer q (1 ≤ q ≤ 2 ⋅ 10^5) — number of points to check.

Next q lines contain two integers per line: x_i and y_i (1 ≤ x_i, y_i ≤ 10^9) — points to process.

Output

Print q lines. The i-th line should contain one real number — total time of the i-th point being in the shade, while the light source is moving from (a, s_y) to the (b, s_y). The answer is considered as correct if its absolute of relative error doesn't exceed 10^{-6}.

Example

Input

-3 1 6
2
2 4
6 7
5
3 1
1 3
6 1
6 4
7 6


Output

5.000000000000000
3.000000000000000
0.000000000000000
1.500000000000000
2.000000000000000

Note

  * The 1-st point is always in the shade; 
  * the 2-nd point is in the shade while light source is moving from (3, -3) to (6, -3); 
  * the 3-rd point is in the shade while light source is at point (6, -3). 
  * the 4-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and at point (6, -3); 
  * the 5-th point is in the shade while light source is moving from (1, -3) to (2.5, -3) and from (5.5, -3) to (6, -3); 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
double s, a, b, l[200005], r[200005], sum[200005], q, x, y, p1, p2, tt;
int u, v, i, n;
const double eps = 1e-9;
int main() {
  scanf("%lf%lf%lf", &s, &a, &b);
  scanf("%d", &n);
  for (i = 1; i <= n; i++) scanf("%lf%lf", &l[i], &r[i]);
  sum[0] = 0;
  for (i = 1; i <= n; i++) sum[i] = sum[i - 1] + r[i] - l[i];
  scanf("%lf", &q);
  for (i = 1; i <= q; i++) {
    scanf("%lf%lf", &x, &y);
    p1 = (x * s - a * y) / (s - y);
    p2 = (x * s - b * y) / (s - y);
    u = lower_bound(l + 1, l + n + 1, p1) - l;
    v = upper_bound(r + 1, r + n + 1, p2) - r;
    v--;
    tt = sum[v] - sum[u - 1];
    if (u - 1 > 0 && r[u - 1] >= p1) tt += r[u - 1] - p1;
    if (v + 1 <= n && l[v + 1] <= p2) tt += p2 - l[v + 1];
    if (tt < eps)
      printf("0.000000000\n");
    else {
      printf("%.9f\n", (b - a) * tt / (p2 - p1));
    }
  }
  return 0;
}